Question

A plane traveled 756 miles each way to Baltimore and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 9 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answer 1

The speed of the wind is 12 miles per hour.

Step-by-step explanation:

Let's call the speed of the plane in still air "p" and the speed of the wind "w".

From the given information, we know that:

756 miles = 7 hours * (p + w) (with the wind)

756 miles = 9 hours * (p - w) (against the wind)

We can simplify these two equations by dividing both sides by 7 and 9, respectively:

108 miles/hour = p + w

84 miles/hour = p - w

Now we can use a system of equations to solve for p and w:

p + w = 108

p - w = 84

Adding these two equations, we get:

2p = 192

Dividing by 2, we get:

p = 96

So the speed of the plane in still air is 96 miles per hour.

To find the speed of the wind, we can substitute p = 96 into either of the simplified equations:

p + w = 108

96 + w = 108

Subtracting 96 from both sides, we get:

w = 12

So the speed of the wind is 12 miles per hour.

Therefore, the speed of the plane in still air is 96 miles per hour and the speed of the wind is 12 miles per hour.